The most common technique for forming circuit elements on a semiconductor wafer is by photolithographic printing whereby one or more reticles (also more commonly called masks or photomasks) are used to form a pattern and selectively expose areas of photosensitive resist layers on the wafer. As integrated circuits become more complex, the number of circuit elements to be created on a wafer become increasingly large and each object becomes correspondingly smaller. As the size of the objects to be created become similar in size or smaller than the wavelength of light used to illuminate the wafer, distortions occur whereby the pattern of objects formed on the wafer do not correspond to the pattern of objects defined by the mask. One objective criterion that defines how well an image is formed or an object is created is the edge placement error (EPE) that indicates how far an edge of an object is shifted from its desired position. Another objective criterion is the edge contrast or slope that describes how sharply the image intensity changes from exposed to not exposed, or vice versa.
To improve the manufacturability of target layout designs, optical process correction (OPC) techniques have been developed that alter a mask layout pattern in order to correctly create the desired pattern of objects on a wafer. The conventional OPC method of improving the fidelity of a layout is to simulate how a pattern of polygon fragments fabricated on a mask will be lithographically reproduced as corresponding edges on the wafer, and then moves the fragment such that the edge on the wafer will be created at the proper location.
In a typical OPC procedure, a target layout comprising several polygons represents the objects desired on the wafer. As shown in FIG. 1A, the polygons 1 in this layout are divided up into several edges 2a, 2b, 2c, etc. For each of the edges, a simulation site 3c, 3d, etc. (also called a control point) is designated. Some edges may have more than one simulation site, although typically there is one site per edge.
A simulation of the image that will be formed if the target layer is used as the mask layout is then run. Simulations are generated at each of the sites of the edges, usually along a cut line perpendicular to the edge, and measurements of the predicted image slope, maximum and minimum intensities are calculated as shown in FIG. 1B. From these image parameters, the actual placement of the edge is predicted using techniques such as the variable threshold resist model, or other simulation techniques. The edge location as predicted and the location of the ideal edge in the target layout are then compared, and the difference calculated as an edge placement error (EPE).
Changes are then made in the mask layout to minimize the EPE. For each edge, a fragment in the mask layout is designated, and each mask fragment is moved in an attempt to reduce the EPE. New simulations at the sites are then generated from the revised mask layout, and new EPEs calculated. This procedure is repeated iteratively until the EPE is small enough, i.e., is within a certain tolerance value.
It has since been recognized that a fragment on a mask often affects more than one corresponding edge on a wafer. Each fragment can potentially affect the creation of many edges that lie within a predefined optical radius. To accurately model these effects, matrix-based computation of the Mask Error Enhancement Factor (MEEF) was developed by Yuri Granik and Nicolas Cobb of Mentor Graphics Corporation, the assignee of the present invention, and others. In matrix-based MEEF computations, the interaction of a single fragment on a mask with many edges to be created on a wafer is considered. In principle, the inverse is also possible, in which the relationship of multiple fragments on a mask with a single edge on a wafer can also be considered. More complex multi-fragment interactions with multi-edge results can also be evaluated.
This matrix formulation can also be applied in the context of OPC. However, in practice, matrix-based OPC has been difficult to implement. First, the matrices that define the relationship between a mask fragment and a number of edges to be created on a wafer are often large and can be difficult to mathematically invert in order to calculate an exact solution for the optimal position of each fragment on the mask. Secondly, an exact solution for each fragment position on a mask does not necessarily ensure the manufacturability of a layout design under a variety of process conditions where variations may occur in illumination, focus, or other conditions. Therefore, there is a need for a method of enhancing the manufacturability of a target layout under a variety of process conditions that takes into consideration each mask fragment's effect on multiple edges on a wafer.